A couple of options springs to mind.
1. The SDSF XDC line command can save a output file to a dataset in one go. The dataset can then be FTPd.
2. Access the log using SDSF SE line command, write an edit macro to pull
the data and send via FTP.
3. Use the SDSF REXX API in a batch job to pull the data. There are good examples in the SDSF manual. As you have a lot of jobs this is probably the way to go.